What is 4/14 plus 7/9?
4/14 plus 7/9 equals 67/63 (or 1 4/63 as a mixed number) (or 1.063492 in decimal form). Learn the step-by-step solution to add 4/14 and 7/9 using Least Common Denominator and simplification.
Exact Answer
4/14 + 7/9 = 67/63
Simplified Fraction
67/63
Mixed Number
1 4/63
Decimal Value
1.063492
Percentage
106.3492%
Step-by-Step Solution: 4/14 + 7/9
Step 1
Find the Least Common Denominator (LCD)
The denominators 14 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 14 × 9 = 126.
LCD(14, 9) = 126
Step 2
Convert to Equivalent Fractions with Common Denominator 126
Multiply the numerator and denominator of 4/14 by 9, and multiply the numerator and denominator of 7/9 by 14 so both fractions share the common base 126.
4 × 9/14 × 9 = 36/126 and 7 × 14/9 × 14 = 98/126
Step 3
Add the Numerators
Now add the numerators (36 + 98 = 134) and keep the common denominator 126 unchanged.
36 + 98/126 = 134/126
Step 4
Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 134 and 126, which is 2. Divide both the numerator and denominator by 2.
134 ÷ 2/126 ÷ 2 = 67/63
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (67) is greater than the denominator (63), divide 67 by 63: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/63.
67/63 = 14/63
Step 6
Decimal & Percentage Representation
Dividing the numerator 67 by denominator 63 produces a repeating decimal (approximately 1.063492, or 106.3492%).
67 ÷ 63 = 1.063492 (106.3492%)
Visual Representation
The diagram below illustrates 4/14 plus 7/9 visually:
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Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 67/63 |
| Mixed Number Form | 1 4/63 |
| Decimal Form | 1.063492 |
| Percentage | 106.3492% |
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Frequently Asked Questions
What is 4/14 plus 7/9 as a fraction?
4/14 + 7/9 in simplest fraction form is 67/63 (or 1 4/63 as a mixed number).
What is 4/14 plus 7/9 as a decimal?
4/14 + 7/9 converted to a decimal is 1.063492.
What is 4/14 plus 7/9 as a percentage?
4/14 + 7/9 expressed as a percentage is 106.3492%.
How do you write 4/14 plus 7/9 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 67/63 can be written as the mixed number 1 4/63.
Does 4/14 plus 7/9 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.063492...) because the denominator contains prime factors other than 2 and 5.